Grade 11 Math: Inequality Word Problems

Inequality Word Problems

Read each word problem carefully. Set up an inequality to represent the situation, solve it, and graph the solution on a number line where applicable. Show all your work.

1. A store sells T-shirts for $15 each. They need to sell enough T-shirts to cover their monthly expenses of $1200. How many T-shirts, x, must they sell to make a profit?

Graph your solution on the number line below:

2. Sarah wants to save at least $500 for a new laptop. She currently has $150 and saves $35 per week. How many weeks, w, will it take her to save enough money?

3. The ideal temperature for a certain chemical reaction is between 25°C and 35°C, inclusive. Write a compound inequality to represent the ideal temperature, T, and graph it on the number line.

4. A projectile is launched upward from a platform 10 meters high with an initial velocity of 20 m/s. Its height h (in meters) after t seconds is given by the equation h(t) = -5t^2 + 20t + 10. During what time interval is the projectile at a height of at least 25 meters?

5. A company manufactures smartwatches. The cost C (in dollars) to produce x smartwatches is C = 50x + 1000. The revenue R (in dollars) from selling x smartwatches is R = 150x. The company wants to make a profit of at least $2000. Which inequality represents this situation?

6. If a business wants to maximize its profit, it should ensure its revenue is   than its cost.

7. When solving an inequality, if you multiply or divide both sides by a negative number, you must   the inequality sign.